Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.stream.LongStream;
import java.io.BufferedWriter;
import java.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.stream.Collectors;
import java.util.List;
import java.util.stream.Stream;
import java.util.Map;
import java.util.Map.Entry;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DMaximumAverageSets solver = new DMaximumAverageSets();
        solver.solve(1, in, out);
        out.close();
    }

    static class DMaximumAverageSets {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int a = in.readInt();
            int b = in.readInt();
            long[] v = in.readLongArray(n);

            List<LongLongPair> list = Arrays.stream(v).boxed()
                    .collect(Collectors.groupingBy(x -> x, Collectors.counting()))
                    .entrySet().stream()
                    .map(e -> new LongLongPair(e.getKey(), e.getValue()))
                    .sorted(Comparator.reverseOrder())
                    .collect(Collectors.toList());

            long p = 0;
            long q = 1;
            long count = 0;
            for (int i = a; i <= b; i++) {
                int use = 0;
                long sum = 0;
                for (LongLongPair pair : list) {
                    if (use + pair.second < i) {
                        sum += pair.first * pair.second;
                        use += pair.second;
                    } else {
                        long c = 1;
                        long add = i - use;
                        for (int j = 0; j < add; j++) {
                            c *= pair.second - j;
                            c /= j + 1;
                        }
                        sum += pair.first * add;
                        if (p * i < sum * q) {
                            count = c;
                            p = sum;
                            q = i;
                        } else if (p * i == sum * q) {
                            count += c;
                        }
                        break;
                    }
                }
            }

            out.printLine((double) p / q);
            out.printLine(count);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public long[] readLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = readLong();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class LongLongPair implements Comparable<LongLongPair> {
        public final long first;
        public final long second;

        public LongLongPair(long first, long second) {
            this.first = first;
            this.second = second;
        }

        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            LongLongPair pair = (LongLongPair) o;

            return first == pair.first && second == pair.second;
        }

        public int hashCode() {
            int result = Long.hashCode(first);
            result = 31 * result + Long.hashCode(second);
            return result;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(LongLongPair o) {
            int value = Long.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Long.compare(second, o.second);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }
}